How Do I Fix Mac OS Can't Repair The Disc Home Folder?

As the message suggests, you should back up your computer and then perform a format work then. Provided that you can save no changes to your Mac, you're suggested to make a copy of the files and data on your device and then drag them to the backup drive. When the data backup work ends, you can launch Disk Utility to format the hard drive in Recovery Mode.

Note that this method wipes everything on your Mac so you have to back up all important files in advance. You can now reset your Mac without losing data here:

Step 1: Click the Apple () symbol in the top left corner of your Mac's screen and select Restart.

Step 2: Click Restart.

Step 3: Hold down the Command + R keys as soon as you hear the Mac tone indicating a reboot.

Step 4: Wait for the macOS Utilities screen to appear, then click Disk Utility.

Step 5: Choose your Mac's system drive and then click Erase.

Step 6: Select the Format option Mac Extended (Journaled).

Step 7: Click Erase, confirm the action if prompted, and wait until formatting is complete.

Step 8: Next, close Disk Utility and click Reinstall macOS.

Step 9: Follow the installation prompts and allow the procedure to continue until you see the Setup Assistant appear.

Step 10: Press the keys Command+Q to shut down your Mac.